INT. J. SCI. EDUC.

2000, VOL. 22,

Exploring the relationship between subject

J. Parker and D. Heywood, Department of Science Education, Manchester

Metropolitan University, Manchester, UK, e-mail:J.Parker@mmu.co.ukThis study explores the tension between subject knowledge and pedagogic content knowledge in primary teacher education. It documents students and in-service teachers learning about forces within thecontext of floating and sinking. In doing so it describes not only significant features of the learningprocess itself but also examines subject specific aspects of learning, identifying some of the inherentdifficulties for learners within this domain and demonstrating how learners construct links between tacitknowledge and abstract scientific notions. Implications for teacher education and the teaching of sciencein the classroom are explored.

IntroductionThe introduction in 1998 of the Initial Teacher Training National Curricula inEngland and Wales (DFEE 1998) situates teacher knowledge at the centre ofaspirations to raise professional status and standards in teaching. For primaryteachers, the statutory requirements specify `the essential core of knowledge,understanding and skills required for entry into the profession. This encompassesthree categories: `effective teaching and assessment methods, `pedagogical knowledge and understanding and `subject knowledge and understanding. In science,the latter presents concerns for teachers education with respect to the nature ofcourse provision where particular difficulties arise in addressing the tensionbetween subject knowledge and conceptual understanding.It is in supporting student teachers in acquiring content knowledge in sciencethat this tension manifests itself most acutely. The concerns are not simply inknowing something (e.g. that the seasons are caused by the tilt of the earth saxis), but in having a coherent, causal explanation which makes sense to theteacher such that they feel skilled in teaching the concept to children. In thisrespect, it is therefore necessary to discriminate knowing from understanding andto identify the implications of this for course provision in Initial Teacher Training(ITT). To fail to do so accentuates a bias towards transmission notions of curriculum delivery in which the focus of student auditing of their own learninginvolves coverage of, rather than engagement with, scientific phenomena.However, to argue that this is in large part a consequence of an overcrowdedInternational Journal of Science Education ISSN 0950-0693 print/ISSN 1464-5289 online # 2000 Taylor & Francis Ltdhttp://www.tandf.co.uk/JNLS/sed.htmhttp://www.taylorandfrancis.com/JNLS/sed.htm

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science syllabus misses the point. What is important is to recognize that in purposefully discriminating between the acquisition of knowledge and the development in understanding, there is opened a fruitful avenue of exploration forresearch into the complex relationship between pedagogy and subject. That professional dimension which demands of the teacher not only subject knowledge andunderstanding, but also knowledge and understanding of the learning processitself. It is, therefore, through direct research inquiry towards the learning processwithin specific domains, that the potential for supporting course provision is likelyto be optimized.The cause for concern in Section C of the ITT curriculum, `TraineesKnowledge and Understanding in Science , rests with the fact that the contentcannot be addressed fully through direct teaching within the time constraintsimposed on current courses. And yet it can be argued that a detailed understandingof the learning of scientific concepts forms the basis from which good scienceteaching might be developed in the classroom.Section A, `Pedagogical Knowledge and Understanding, required by traineesin order to secure pupils progress in understanding of `key scientific ideas and therelationships between them, in effect demands a complex cognitive synthesis ofideas encountered in section C with the learning process itself. It demands asubtle, in-depth knowledge of scientific phenomena involving, for example, thenature of and relationship between pupils ideas and scientific explanations, howideas might be developed and the use and limitations of models, illustrations andanalogies in learning.It is our contention that development of such knowledge and expertise is infact a lengthy process for most learners requiring considerable intellectual andpractical engagement on a personal level and that different subject specific areasmay have different characteristics which the learners need to be aware of. Whatmight be involved in developing these context specific scientific ideas and thepossible implications for teaching and learning science require examination ofboth subject and pedagogy. And more importantly, how in the learning process,each needs to be explicitly recognized by the teacher. First then, the issues inscience subject knowledge.The debate about teachers subject knowledge has been fuelled through avariety of research approaches. Such studies have concerned not only teachersideas with respect to a variety of science concepts but also consideration of howthese might be developed and what sort of knowledge teachers might need in orderto become effective practitioners.Several studies have demonstrated that primary teachers may often lack apersonal scientific background on which to draw and that, indeed, many maythemselves hold misconceptions of current scientific ideas. This is particularlyevident in the area of physical sciences (see for example Kruger et al.(1990a,b,c) Kruger and Summers 1989, Summers 1992, Solomon 1992, Mantand Summers 1993, Parker and Heywood 1998). Clearly, therefore, one purposeof teacher education must be concerned with the issue of helping teachers todevelop their own understanding about scientific concepts. However, this is notthe only prerequisite for successful science teaching and, important though it is,knowing the subject does not necessarily translate into effective teaching of thatsubject. This raises a second issue, that of professional insight into the learning and

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teaching of the subject, which has been identified over the last decade as pedagogicknowledge.Shulmans (1987) notion of pedagogic content knowledge implies that ifteachers are to be effective practitioners they need to possess an in-depth knowledge of how to represent the subject matter to learners. This is predicated onteachers subtle and detailed knowledge of the subject matter itself. Indeed, ithas been demonstrated that teachers do in fact draw upon a complex array ofvarious types of knowledge in promoting effective learning. For example, Barbaand Rubba (1992) found that experienced teachers brought more declarativeknowledge to the problem, used more steps to solve a problem and generatedmore sub-routines and alternative solutions in doing so than did novice practitioners.The past 20 years have seen major efforts in physics education to identifystudents ideas about scientific phenomena, both prior to and following formalinstruction (Carmichael et al. 1990, Pfundt and Duit 1991, Driver et al. 1994).That scientific understanding cannot simply be transferred through the use ofwords but is constructed actively on a personal level by the learner, is supportedby the plethora of reserach findings under the broad umbrella of constructivism.In such a so-called constructivist framework of teaching and learning, knowledgeof students conceptions becomes central and there is an impressive body ofresearch knowledge to identify both childrens and adults notions about a hostof scientific ideas. However, a Niedderer et al. (1992) point out, very few studieshave focused on the teaching and learning process itself and yet a constructivistparadigm requires that teachers have knowledge of how the ideas of studentsemerge during the learning process. This represents a shift in research focusfrom pre/post `snapshots of understanding to `strobe pictures of the learningprocess in action. Dykstra (1992) reiterates this when considering the importanceof questioning student beliefs and introducing disequilibrations into learning:`Effective development and utilization of pedagogy requires a better and moredetailed understanding of conceptual change than has previously been described(p.41).This study aimed to provide an insight into the process of knowledge acquisition when primary teachers and student teachers were engaged in the learning ofthe difficult and abstract notion of forces. As Dykstra observed, this is a particularly challenging area for learners where `simply presenting students with aNewtonian view of the world however perspicuous and sequenced is not usuallysufficient for getting them to change their thinking about how the world works(p.41).There is extensive research literature into learners ideas about forces, (for auseful summary see Driver et al. 1994), which document well the inherent difficulty in developing knowledge and understanding of what might be described asthe counter intuitive Newtonian view of the world. Common ideas identified are,for example, a strong association in learners minds between force and motion,force being an entity which belongs to an object and force being a finite quantitywhich is capable of being used up. Such ideas are often deeply embedded inlearners wide ranges of personal experiences of the world and they are notoriouslydifficult to shift. Often such notions are held alongside `scientific ideas , whichlearners usually fail to apply on reflection.

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Gunstone and Watts (1985) stress the need for students to have ample time for therestructuring of new ideas offered in a form that needs to be both intelligible andplausible. Several studies identify useful teaching approaches. For example Minstrell(1982) and Brown (1994) propose the use of bridging analogies between learners priorideas and scientific ideas in order to help them to make logical and sensible connections between the two. Finegold and Gorsky (1991) stress the need to help pupils toextract general rules from instances and apply general rules to instances. Others suggest that learners need to see that their ideas are unsatisfactory (Dykstra 1992) anddevelop concrete rather than abstract anchoring conceptions (Clement 1993). Studiesin other conceptual areas have raised the notion of enabling concepts (Sharp 1996)used in a hierarchical fashion in order to facilitate the construction of meaning from anintuitive egocentric view of the world to an abstract remote view of the earth in space.The present study is part of a long-term research inquiry exploring ITTstudent and in-service teacher learning about forces. It focuses on the phenomenonof floating and sinking, an area with a long historic tradition in British primaryschools beginning with exploratory play in early years and currently extending intolearning about forces in the later primary years. In the national curriculum forprimary science education (DFEE 1995) at key-stage 2 (7-11 year olds), floating isgiven as a specific example to help children develop the notion of balanced forces.In order to underpin teaching about forces the teacher training national curriculum (DFEE 1998) demands that students are required to understand that:. when an object is stationary or moving at a steady speed in a straight line,forces acting on it are balanced;. balanced forces produce no change in the movement or shape of an object,whereas unbalanced forces acting on an object can change its motion or itsshape;. the change in movement and/or shape of an object depends on the magnitude and direction of the forces acting on it.It has long been accepted that this is a challenging area for learners and indeed theInstitute of Physics (see Campbell 1998) has recently challenged its very place inthe primary curriculum.The following study therefore explores student learning through a series ofactivities designed to develop subject knowledge with respect to the statedTeaching Training Agency (TTA) requirements. In addition it identifies individuals perspectives on key features of learning within this domain. In doing so itoffers an insight into what is involved in effective science teaching through identifying those elements which support the synthesis between pedagogy and subjectknowledge and understanding.The Study: MethodologyThe research involved two groups of students undertaking a one-year course leading to a Post Graduate Certificate in Education (PGCE) for primary teachingcomprising 44 students in total. A second group of learners (30 in total) wereprimary teachers on an in-service course designed to enhance teacher subjectknowledge and understanding in order to support the effective meeting of thenational curriculum requirements for science in the primary classroom. The background knowledge and experience of course members varied, with PGCE students

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having a range of first degree expertise and primary teachers, many of whom werescience co-ordinators, with experience of various levels of teaching within theprimary sector. Although most of the teachers had little experience of forces intheir own educational background they had, nonetheless, all experienced someteaching relating to floating and sinking during their school careers.The study aimed to identify how learners thinking was influenced as theyundertook a variety of activities based on floating and sinking. The activities weredesigned in order to provide opportunities for students to:1. experience forces in a physical way;2. help them to generate ideas concerning factors which might influence floating and sinking;3. develop and explore their own hypotheses about why some objects floatwhile others sink.The activities employed a range of approaches from directed to open and involvedthe students in recording responses to specific questions as well as personal observations and reflections. Indeed, personal reflection on the teaching/learning process has emerged in past decades as being a fundamental part of teacher education.Leat et al. (1992) regard student reflections on experience as providing not onlyinvaluable data on course outcomes but also assisting in the learning process itself.The rationale underpinning this process has, in the past proved very successfulin helping students to become aware of their own thinking and how their ownlearning has taken place (Parker and Heywood 1998). This is predicated on theneed for teachers to recognize significant elements influencing their learning suchthat they might draw parallels with childrens learning and address identified keyfeatures of learning that are problematic in promoting understanding in particularconceptual areas.

The activities1. Pushing an inflated balloon into a tank of waterThe aim of this activity was to enable students to experience forces in a physicalway prior to considering them in a more abstract manner. They were introduced tothe notion of forces as pushes and pulls and asked to note what they observed fromthe activity. This was followed by a class discussion of observations with particularreference to the notion of weight as a force, upthrust, equal and opposite forces andforces in balance in a floating object.2. Exploration of a range of everyday objects with respect to floating andsinkingLearners were provided with a range of everyday objects and asked to predictwhether or not they would float prior to testing. This directed activity enabledstudents to bring to bear their personal experience in making predictions andthrough the deliberate introduction of some less obvious objects (e.g. candle,plastic counters), to promote thinking about the causes of floating and sinking.

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At this stage students were asked to produce a list of the factors they thought mightbe influential in the situation.3. Large, heavy floaters and small, light sinkers.Our previous experience of working with learners in this area has shown that thenotion of weight is a central tenet of learners reasoning. Even though most adultlearners recognize that weight is not the only determining factor, it is so deeplyembedded as an intuitive response that they often find it difficult to make progressbeyond this and to articulate their thinking clearly. Consequently objects wereintroduced to deliberately challenge notions of the effect of weight on floatingand sinking and to ascertain whether the students were able to clarify their thinking on the role of weight in this situation as a result. Resources provided included alarge glass jar with a screw cap lid, a block of wood, a large block of solid wax, apaperclip, a small ball of plasticine and a small glass bead. Each student formulatedan initial hypothesis about what they thought determined floating/sinking and thenreviewed/modified this after the practical activity.4. Floating a screw cap jar in a tank of waterA small, empty screw cap jar was floated in a tank of water and students were askedto explore and develop explanations for what would happen as they increased theamount of water in the jar. The purpose of this activity was to facilitate explorationof increasing the weight of the jar whilst keeping the volume constant. Studentswere encouraged to note anything of significance to them during the activity, thismight be in the form of questions arising, significant observations, developingexplanations etc. Reflections were of a personal nature, of significance to the individual and served to reveal something of what might be uppermost in their thinking at that point in time.Finally students were asked to reflect on what they saw as significant in theirown learning. They were to identify key areas of learning with respect to forces,floating and sinking and also to comment on the teaching and learning processitself and to consider any teaching implications arising.

The role of the tutor

The tutors role was to support students in their learning experiences and to helpto orient them into thinking about forces acting. After a brief introduction to thenotion of forces as pushes and pulls, learners participated in activity 1, which wasfollowed by a class discussion of forces acting (gravity, weight and upthrust). Thisculminated in the tutor introducing the notion of balanced and unbalanced forcesacting in floating and sinking respectively. The tutor introduced each activity andthere was a final plenary of significant learning taken from the students perspectives. In the meantime the tutor s role was one of working with groups in order tosupport investigations and focus learning on forces as the following extract of arecorded conversation between tutor (T) and two students (A and B) illustrates:T:

what s happening to the jar? (students are adding water to the small screw capjar);

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A:T:B:T:A:T:B:A:T:B:A:T:B:

gets to the point where it sinks;

so why do you think that happens?it s (the water) making it heavier . . . cos theres less air in it and more water, soit s heavy;has anything else changed?no, it s the same, the jar and everything, it s just got more weight with the waterin;so is it just the weight that makes things float or sink?no it can t be cos the big jar floated didn t it?but if you put water in it, it would sink eventually;so what can you say about it then?it just gets too heavy . . . for its size;yes, it must be both things really;what can you say about the forces?well it (the weight) just gets bigger and the push back (upthrust) cant keep it upanymore.

ResultsActivity 1Initially there was general uncertainty within the learning groups about floatingand sinking, particularly with respect to the notion of forces.Why is it so difficult is it the balloon or the water?Is the resistance from the water or from the air in the balloon?

The physical experience of pushing a balloon into a tank of water generated considerable surprise even amongst experience teachers (table 1).It was surprising to feel such a strong resistance from such a light object.

Table 1. A summary of students responses to activity 1

Responseexpressed surprise at how difficult itwas to push balloon into waterreferred to resistance/pressure of waterused the term force to describe theupthrust of the waterreferred to push back/upthrust/upwardthrustrecognized that it was harder to push theballoon further into the waterstated explicitly that as the downwardforce was increased so the upthrustincreasedrecognized water level rising/water beingdisplacedrecognized it was easier to push the balloonnarrow end first into waterreasons given:surface areacapacity/volume

PGCE Students(n 44)

Teachers(n 30)

22 (50.0%)

17 (56.7%)

20 (45.5%)2 (4.5%)

3 (10.0%)14 (46.7%)

10 (22.7%)

9 (30.0%)

16 (36.4%)

4 (13.3%)

2 (4.5%)

1 (3.3%)

44 (100%)

20 (66.7%)

36 (81.8%)

14 (46.7%)

9 (20.5%)2 (4.5%)

00

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Most comments centered on the immediate physical impact (for example, `theballoon feels harder, like it might burst ) with PGCE students tending to refermore to the `resistance or `pressure of the water and teachers focusing more on`push back/upthrust/upward thrust/upward force/counter force . Students commented on the water level rising as the balloon was pushed in or water beingdisplaced and many noted that it was easier to push the balloon into the waterwith the narrow end first. Only 11 students offered explanations as to why thismight be, focusing mainly on notions of surface area (9) and volume (2). Fourlearners demonstrated notions of the balloon `wanting to escape:Why is it so difficult to submerge the balloon? possibly because it naturally wants tofloat, in other words we are attempting to force the balloon to sink when if it is leftalone it would naturally float.The balloon tries to move to the side and get back up where it belongs.

Others sensed that it was `something to do with a variety of factors but they foundit difficult to be explicit about the nature of the relationship between them, expressing an almost intuitive feel for the situationThe force is extremely strong it s something to do with density and surface area. Itmust be something to do with the amount of water displaced.

Teachers were more likely to engage in a discussion of forces which is hardly

surprising since in the national curriculum floating is given as a specific exampleof balanced forces.The volume of the balloon displaces the water and the force of the water pushes theballoon back to the surface.

Fourteen out of 30 teachers stated explicitly that the water was responsible forproviding a `push back whereas only two of the PGCE students made such linksexplicit in their writing. Several learners noted that it became more difficult topush the balloon further into the water but only three people made explicit reference to a relationship between the size of the downward force and the size of theupward force. Some saw the situation as a `battle of forces :The balloon resists the water as it battles the upthrust.

Activity 2As table 2 demonstrates learners readily identified a host of factors which mightinfluence the floating of an object. Shape, surface area, air content, density, weightand material from which the object was made, all featured prominently in theirthinking. It was interesting to note that ten learners referred to the size of theobject while 56 referred to its shape. Only nine learners in total associated morethan one factor within a relationship and only three attempted an explanation interms of forces, illustrating that floating and sinking is not, for most learners, asituation in which they would naturally apply the concept of force. Of those associating two factors most identified weight as one of the factors. Three referredspecifically to density with respect to the size of the object, implying that theirnotion of density was associated with the nature of the material from which theobject was made, as opposed to the density of the object itself. Thirty-two of the

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J. PARKER AND D. HEYWOOD

prior to and following participation in activity 3. Initial hypothesisbased on one determining factor (n 44).Initial hypothesisWeight6 students (13.6%)

Air content8 students (18.2%)

Surface area4 students (9.1%)

Solid/hollow object1 student (2.3%)Density1 student (2.3%)

Post activity hypothesis

..............

weight in relation to size (1)

weight and size (density) (1)weight and size (2)weight per size (1)air content (not weight alone) (1)no change (5)weight is irrelevant (1)spread of weight and size (1)how closely packed the molecules are (1)weight and density (1)weight and surface area (not weight alone) (1)air and type of material (1)object floats on largest surface area (1)spread of weight and size (1)

. weight and air content together (1)

PGCE students focused on the surface area of the object with only two studentsreferring to volume.Activity 3Results are only available for the PGCE learning group for this activity. Studentsworked in small groups in order to develop an initial hypothesis on why objectsfloat or sink in water; following the exploration they reviewed and amended theiroriginal thinking. Outcomes are summarized in tables 3a and 3b. Table 3a relatesto students using one determining factor in their initial hypothesis and table 3billustrates those using two or three.Analysis of conceptual change revealed no distinct and predictable outcomeson an individual basis. Rather, the data reflect the complexity of learning withstudents starting from the same apparent point, working together on the sameactivity and yet identifying different aspects of significant learning. It is possible,however, to detect some general points of importance.Firstly, the results reflect the centrality of the notion of weight in learnersreasoning (52.3% cited this parameter), with air content and surface area alsofeaturing prominently (43.2% and 38.6% respectively). A total of 45.4% of studentsemployed only one determining factor with 36.4% citing two and 18.2% three.Weight, air content and surface area featured significantly in most hypotheses,usually being linked with some aspect of size and shape. The term density wasemployed less frequently (18.2%) and it was most often associated with air contentand/or various aspects of size and shape which suggested that it might refer to thematerial composition of the object (excluding air content) as opposed to the objectitself.

. weight and surface area (size),

. air content (1)

. air content (weight unimportant)

Post activity hypothesis

Table 3b. Changes in PGCE student explanations of floating and sinking prior to and following participation in activity 3.Initial hypothesis based on two or three determining factors (n 44).

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J. PARKER AND D. HEYWOOD

This activity was largely successful in focusing attention on the role of weightin floating and sinking and as a result there is a general movement towards thelinking of weight with size (or some aspect of size). The term surface area was oftenincluded in reasoning and some reflections revealed evidence that this was associated with the view that upthrust was a finite entity that resided in water, thereforethe greater the surface area, the larger the area over which upthrust might act:The larger the surface area the greater the area for the upthrust to push on.

Some students began to move towards a notion of density. For example, table3a shows clearly a student operating on weight as the determining factor progressing to an association of weight with size and in turn relating this to density. Somestudents related density to how closely packed the molecules of materials were andhad begun to incorporate air into their reasoning.The activity seemed to be less useful for those with initial hypotheses dependent on the air content of the object. Some reasoned that as the three small objectscontained no air then the large floating objects must contain large amounts of aireven if it could not be seen directly:Although you can t see it, there must be lots of air in the wood and the wax so thatthey can float.

The extent to which learners viewed air as a light material as opposed to an

uplifting force was unclear but written reflections did contain evidence of both:Air is buoyant, it makes things float up.Air is light because of its loose molecules.

It was interesting that some students who began with a hypothesis based on weightand air displayed a range of learning outcomes. Two learners subsequentlyrestricted their view to air alone; others changed their views to incorporate weightcombined with size and density. Where weight, density and air content had beencited initially then air content emerged a the significant factor. In everyday experience objects with large air capacities tend to float, such logic is likely to be deeplyrooted and may require considerable challenge.Activity 4This activity involved exploring and thinking about what happens when water isadded to a screw-cap jar. Learners were invited to make personal reflections of anopen nature and consequently were examined qualitatively. A variety of responseswere recorded with some learners listing questions which were concerning them,others reporting what they saw as significant observations and others describingtheir own explanations for what was happening. Several categories can be discerned:(i) General why questionsThese seemed to represent initial thoughts and were usually of the type:Why is the jar floating like that?Why does it sink past a certain point?

(ii) Relevant observations

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For example, some focused not on the floating/sinking of the jar but on the sideways position of the empty jar in the water.I don t know why but I know it will (fall on its side).

(iii) ExplanationsLearners explanations were often tentative, in the form of questions e.g.:Is it because there are 2 materials of different densities? (glass-jar, metal-lid)Is the glass bottom heavier than the metal top?

Others tried to explain the situation in terms of forces with some engaging indiscussion of equal and opposite forces in balance in a floating object.I think it s to do with the centre of gravity.The downward force is the weight and the water gives back an equal and oppositeupthrust, these two forces are in balance when it floats in the water or rests on thebottom of the tank.

Again there were notions of the amount of force being associated with the surfacearea of the object:On its side - bigger surface area - more space for the water to push on.

Also there were notions that the forces might be unevenly distributed on the jaritself:Is there more upthrust on the end that s higher in the water?

Adding water to the jar, thereby increasing its mass whilst keeping its volumeconstant and exploring the effects systematically seemed to help students developtheir ideas more clearly. Some focused on what was happening when the amount ofair in the jar was changed:The trapped volume of air keeps the jar light for its size. When it s half full of waterit s heavier volume of air is reduced but still light for its size (density) so it floatslower in the water.When changing the amount of water in the jar we looked at it with a view that wechanging the amount of air, making it heavier.Is the floating to do with the amount of air or the amount of water in the jar?

Others seemed to have developed a clearer sense of the notion of density:

The jar floats lower in the water cos it s now more dense.Adding water increases its mass for size (density).You can make the jar float by decreasing the water in the jar, i.e. making it lighter forits size more dense.

Some developed a clearer notion of opposing forces in balance but often termssuch as mass, weight and gravity seemed to be used interchangeably:Forces acting on jar = downward - weight and upthrust - in balance when objectfloats.Gravity is the downward thrusting force - the water is the counterforce - causes anupthrust and they balance.

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The bigger the mass/weight, the bigger the downward force.

(iv) Making links with wider experience

For some students part of the process of making sense of the phenomenon involvedmaking links with previous knowledge and experience, this seemed to occurrapidly when students had developed their understanding of balanced forces andthe effects of changing the density of an object.It s just like a submarine isn t it?It ( jar) would float higher in salty water because the salty water s more dense!Salt water would support a heavier weight.Would heavy objects sink to the bottom of the Dead Sea?If we put helium in instead of air it would be lighter and float higher.

Learners perspectives on significant learning

Learners were asked to identify what for them constituted significant personallearning as a result of the activities they had participated in. They were asked tocomment on their understanding of the subject matter itself as well as significantfeatures of the process of teaching and learning. Table 4 summarizes responses forboth serving teachers and PGCE students with respect to subject matter. Keyfeatures were the recognition that although air is important in floating and sinking,it does not actually make objects float. Teachers were more likely to relate thisexplicitly to the notion of weight: size ratio. The concept of weight for size seems tohave been a key feature for many learners. Identifying forces acting, in particular,equal and opposite forces in this situation was also important in learning.Floating and sinking is a conceptual area where an intuitive sense of what ishappening and why is often paramount in learners thinking:Before starting I just `knew what would float and sink.Our first impressions were based on guesswork.I knew about this but I d forgotten.

Comments on the teaching and learning process were immediate and personal. Formany PGCE students, viewing this situation from a forces perspective was something new:I just didn t think about floating and sinking with a view to forces.

Developing a qualitative explanation for something so intuitive and possibly from

a different perspective was, for some, surprisingly difficult:While you may think you know something will either float or sink actually being ableto say why it does is a very difficult task.Density is difficult to explain verbally, it does not follow common sense.It s stuff I ve `learned before but never really thought too much about it and it ssurprisingly hard.

Recognizing the difficulties in their own learning led to identifying implications

for teaching and learning. For example, several students commented that having to

air molecules are lighter than

water moleculesWeightweight alone is not the determiningfactorweight for size determine floatingand sinkingheavy objects must be large inorder to floatobjects heavy for their size willsinksize and weight can be changed toinfluence floating and sinking

Airair is a key factorair is involvedair does not make things float/sinkair changes the weight : size ratioair is lighter than water

(45.5%)

(61.4%)

20

27

(34.1%)

(2.3%)

15

(9.1%)

3(6.8%)015 (34.1%)5 (11.4%)5 (11.4%)

PGCE students(n 44

(73.3%)

(63.3%)

(46.7%)

3 (10.0%)

14

3 (10.0%)

22

19

3 (10.0%)

01(3.3%)18 (60.0%)12 (40.0%)6 (20.0%)

Teachers(n 30

forces act on objects and do not belong

to themwhen forces become unbalanced theobject will sink

recognizes forces in balance

recognizes opposing forces

(6.8%)(22.7%)

10

(72.7%)

(81.8%)

(2.3%)

(4.5%)

(18.2%)(11.4%)(2.3%)(18.2%)(9.1%)

32

36

Materialmaterial object is made from is importantForces

85184

Densitydensity of object is the determining factorweight for size = densityrelates density to mass and volumerelates density to weight and volumerecognizes the effect of changing thedensity of the waterdensity of water = 1

PGCE students(n 44)

22

29

75266

(30.0%)

(13.3%)

(73.3%)

(96.7%)

(3.3%)

(23.3%)(16.7%)(6.7%)(20.0%)(20.0%)

Teachers(n 30)

Table 4. Learners perspectives on significant features of their own learning with respect to floating and sinking.

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shapesurface areaweighthollow/solidmaterialdensity

shapesurface areamaterialsolid/hollowinteraction of allfactors

. balloon felt heavier

in water. strong resistance(in water or air inballoon). water displaced. balloon wants tofloat

. difficult to pushballoon down. water providesresistance. water level rises

Significant learning identified

104J. PARKER AND D. HEYWOOD

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Figure 1.

105

Examples of teachers comments on key features of their own

learning.

I now have a much clearer understanding of things. I have learnt about forces in thepast but have tried to understand them at a higher level without having developed thebasic knowledge. The balloon in the water was an important part of my learning as itmeant that I could actually experience the force of upthrust.By trying experiments on a small scale we were eventually able to make sense of bigquestions such as why does a huge liner float.For me, I never really thought about forces in something stationary and I think this isthe case for children, but experiencing it has been very useful in my own understanding.I realised that when confronted with the question that big things are heavy thing andsmall things are light. I didnt know how to explore this further. In class we weighedthings and identified that this was the case but I wasn t sure where to take it. Theexperiment we did today showed how weight for size is central . . . taking two things atonce.Being able to try out your own hypothesis was the important thing for me.

verbalize thinking and be specific about hypotheses had been a useful part of theprocess.For children I will have to help them to make clear hypotheses . . . otherwise lots ofmessy, pointless filling of jars will happen if there is no clarity of thought about whatis happening.I have learnt the difference between qualitative and quantitative explanation.I can understand how children might struggle with ideas.I now feel there s a lot more to understanding floating and sinking than I first imagined . . . it s the building of ideas and putting them together . . . holding two ideastogether is much harder than holding them both separately.

Many of the PGCE students referred to the need to experience forces in a

physical way and clearly, engagement in practical investigation had been veryimportant. The teachers reiterated the sentiments expressed by PGCE studentswith respect to the need to experience forces in a tangible, physical way and toexplore them in a practical sense but in general they were able to identify moresophisticated implications for teaching and learning. Significant features included:making links from small scale experiments to real life situations; recognizing andexperiencing forces acting in stationary objects as a possible precursor to understanding forces in moving objects; providing challenge and recognizing the difficulty and manipulation in holding two concepts at the same time (see figure 1 forexamples of reflective writing).

Tracking conceptual development across the activities

As observed previously in activity 3 individual progress was difficult to predict,even when students possessed apparently similar starting points the learning outcomes were personal and subtly different. Table 5 illustrates the progress of fourstudents as they undertook the activities provided.

. pressure, forceincreases as theballoon is pushedfurther down. water is beingdisplayed

. extreme forcesneeded to pushballoon down

Activity 2Influentialfactors

Student

Activity 1Balloon observations

air content

surface areavolumesize

Initialhypothesis

Activity 3

air content

weight andsurface area(size)

Post-activityhypothesis

Table 5. (Continued).

Significant learning identified

. gravity pushes down . relationship between weight

. water exerts upthrustand size. adding water. density of the objectincreases densityrelative to water (mass/of jarvolume). air does not make thingsfloat air reduces density. density of water =1. seawater has a higher density,pushes back more. various factors play a role. removing air from. air is the key factorjar makes it sink

Activity 4Jar exploration

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Students A and B worked in the same small group and had similar startingpoints. Student A noted that when the balloon was pushed into the water there wasa strong resistance and wondered whether this was due to the air or the water. Shewas able to produce a considerable range of factors influencing the situation(including density) and yet, interestingly, based her initial working hypothesis inactivity 3 on weight alone. Post activity was revised to weight and size in a relationship (weight per size) which seems to have been confirmed through activity fourand extended to make links with density. There was explicit recognition of manipulation of density in the jar investigation and recognition of the contribution of air.The relationship between weight and size appears to be a significant feature oflearning, which can be related to the balance of forces acting on the jar.Student B had a similar starting point but provides less comment on density inthe early stages. Activity 3 results in the association of weight and size with thenature of the relationship (if any) remaining unclear at this point. Activity 4 seemsto be instrumental in developing the relationship between weight and size and thisis related explicitly to the forces acting. This is reflected in significant learningwhich demonstrates subtle differences with less of a focus on density comparedwith student A and more of a focus on weight for size and forces acting.Student C displayed notions of pressure and force increasing with depth as aresult of activity 1 and produced a comprehensive list of factors during activity 2.His initial hypothesis for activity 3 was based on surface area, volume and density,which was subsequently amended to weight and surface area. Activity 4 resulted inengagement with development of a forces explanation and this was linked withdensity. Significant learning displays strong links with existing knowledge, particularly density.Only two students in the sample did not appear to make progress with respectto developing their ideas of forces acting. This is illustrated with reference tostudent D. Beginning with the observation that a large force is needed to pushthe balloon down in activity 1 and presenting a wide range of influential factors inactivity 2, the central hypothesis in activity 3 (air content) remains intact and isconfirmed by activity 4, where the addition of water is interpreted as removal of airleading to the sinking of the jar. There is no discussion of forces involved and airremains the significant feature with various other factors playing an undefinedrole.DiscussionThis study describes in detail some of the complexities of learning pertaining toboth process as well as subject specific elements. These features characterize theconceptual demands of engaging intellectually in learning situations. Through acombination of structured and open questions, personal reflection and practicalinvestigation it was possible to explore not only how learners reasoned aboutfloating and sinking, but also how that thinking was influenced through the teaching and learning experiences they encountered. Consequently students were ableto identify valuable implications for their own teaching.Dart et al. (1998), in discussing the evidence that many university studentsemerge from degree courses with little but surface declarative knowledge of theirdiscipline, raised a highly significant concern with respect to teacher education. Ifteachers are to become effective practitioners their education must equip them

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with a deep knowledge of significant factors which influence learning. The implications are not only a requirement for in-depth subject knowledge but, as Dartet al. point out, as beliefs about teaching and learning drive decisions to do withteaching (Biggs 1989), prospective teachers need an awareness of the nature oflearning itself.

Key features of the learning process

Initial thinking about forces was often vague with intuitive thinking and tacitknowledge playing a dominant role:I just knew what would float and sink.

Learning is a complex process, highly personal and difficult to predict. As table 5

illustrates, significant differences in learning emerge in students undergoing similar learning experiences. This accords with von Glasersfeld s (1992) view of constructivist learning in that teaching is a social activity but learning is a privateactivity with understanding being constructed by each individual `knower . Thelearning agenda is clearly set by the learner herself and the challenge for theteacher becomes one of how best to facilitate the learning within that personalframework of reference.It has long been recognized that intuitive/common-sense/naive ideas and alternative conceptions are often firmly embedded in peoples minds and that they canbe stocially resistant to change (Brown and Clement 1987, Steinberg 1990, Driveret al. 1994). If learners are to make conceptual progress in scientific thinking thenwe need to know more about the specific details of what facilitates the process.Learners reflections revealed some important insights such as:. verbalizing ideas forced them to confront aspects they were unsure of and torecognize similarities and differences between their ideas and those ofothers;. formulating and testing personal hypotheses;. testing thinking through practical investigation;. reviewing, refining and reformulating thinking in the light of experimentalevidence;Some were able to identify sophisticated elements and their observations included:. explanations are constructed personally by the learner;. subject knowledge required for teaching needs to encompass much morethan scientific fact if teachers are to nurture understanding;. thinking often needs to be challenged conceptually if development is tooccur;. teaching needs to help learners to build connections between tacit knowledge and scientific explanation in relevant and meaningful ways;. the notion of weight for size requires learners to hold together two conceptsin a relationship and this is much more difficult than holding them separately;. developing qualitative explanations for what had formerly been taught in aquantitative way during past education was highly significant in developingunderstanding and empowering the learner.

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ImplicationsThe study has thrown into sharp focus the difference between knowing and developing understanding in science. The latter requires that learners develop and internalize coherent and causal explanations for the phenomena they observe and thishas been supported by research findings in other areas (see for example Parker andHeywood 1998). Explanations must provide learners with a convincing rationalefor their existing observations and ideas about how the world works if they are tomeet the criteria for satisfactory explanations and become part of reasoning strategies. Dillon (1994) in discussing the value of qualitative reasoning in the learningof physics points out that people seem to reason very successfully about physicalsystems where the only knowledge they have is qualitative. Qualitative reasoningconcerns the skills used by expert practitioners to reason about the world in nonquantitative ways. Such qualitative reasoning may have an important role to playin helping learners to develop an understanding of abstract scientific ideas andtranslate this into effective pedagogy.Effective practitioners require not only a personal understanding of subjectmatter but also a subtle knowledge of pedagogical implications for teaching. Thisso-called pedagogical content knowledge (Shulman 1987) covers a host of issuesinvolving for example: how to ascertain and challenge learners ideas in productiveways; knowledge of the inherent difficulties for learners in the learning of a particular subject; what learners might see as abstract notions and how to representthe subject matter in that teaching and learning interface. We have identified andexplored some of these issues in student learning about forces with respect to boththe subject matter and the learning process itself.As we approach the millennium, the nature of science education is underreview and recently the outcomes of a series of seminars on the future of educationwere published in the report Beyond 2000: Science education for the future. (Millarand Osborne 1998). The report examines the successes and failures of education todate and explore what type of science education might be required for the future.In advocating a curriculum to sustain and develop the curiosity of young peopleand to develop the ability to engage with scientific and technical matters, greatemphasis is placed on empowering the learner through developing `scientific literacy . Such literacy implies the development of understanding of fundamentalscientific notions as opposed to the knowing of explanations and details of processes.Golby et al. (1995) criticized research that focuses on teachers weaknesseswith respect to subject matter and the assumption that this can be redressedthrough supplying appropriate subject knowledge, which can then be transferredto children. They make the point that this approach implicitly nurtures a transmission view of teaching and learning science and go on to make the case for aperspective in terms of what teachers can do. Such a focus on teacher capabilitieswill enable the setting of realistic expectations for the classroom. We believe that aclose focus on developing qualitative understanding which links and providescausal explanations for personal experiences must be of significance to teachereducation. The present study demonstrates that through such a process teacherscan and do engage successfully with difficult and abstract scientific ideas. Whatteachers can do effectively, given the opportunity, is to scrutinize closely their ownlearning and in doing so identify the characteristics of the learning process itself

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within specific subject domains. Metacognition refers to the knowledge and regulation learners have of their own thinking and learning (Brown 1987), learningabout learning could contribute to resolving the tension between subject knowledgeand pedagogy.